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48
The Variable Discharge of Cortical Neurons: Implications for Connectivity, Computation, and Information Coding
 J. Neurosci
, 1998
"... this paper we propose that the irregular ISI arises as a consequence of a specific problem that cortical neurons must solve: the problem of dynamic range or gain control. Cortical neurons receive 300010,000 synaptic contacts, 85% of which are asymmetric and hence presumably excitatory (Peters, 198 ..."
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Cited by 219 (1 self)
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this paper we propose that the irregular ISI arises as a consequence of a specific problem that cortical neurons must solve: the problem of dynamic range or gain control. Cortical neurons receive 300010,000 synaptic contacts, 85% of which are asymmetric and hence presumably excitatory (Peters, 1987; Braitenberg and Schuz, 1991). More than half of these contacts are thought to arise from neurons within a 100200 #m radius of the target cell, reflecting the stereotypical columnar organization of neocortex. Because neurons within a cortical column typically share similar physiological properties, the conditions that excite one neuron are likely to excite a considerable fraction of its afferent input as well (Mountcastle, 1978; Peters and Sethares, 1991), creating a scenario in which saturation of the neuron's firing rate could easily occur. This problem is exacerbated by the fact that EPSPs from individual axons appear to exert substantial impact on the membrane potential (Mason et al., 1991; Otmakhov Received Sept. 15, 1997; revised Feb. 25, 1998; accepted March 3, 1998.
Mathematical Formulations of Hebbian Learning
 Biol Cybern
, 2002
"... Several formulations of correlationbased Hebbian learning are reviewed. On the presynaptic side, activity is described either by a firing rate or by presynaptic spike arrival. The state of the postsynaptic neuron can be described by its membrane potential, its firing rate, or the timing of backprop ..."
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Cited by 77 (7 self)
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Several formulations of correlationbased Hebbian learning are reviewed. On the presynaptic side, activity is described either by a firing rate or by presynaptic spike arrival. The state of the postsynaptic neuron can be described by its membrane potential, its firing rate, or the timing of backpropagating action potentials (BPAPs). It is shown that all of the above formulations can be derived from the point of view of an expansion. In the absence of BPAPs potentials, it is natural to correlate presynaptic spikes with the postsynaptic membrane potential. Time windows of spike time dependent plasticity arise naturally, if the timing of postsynaptic spikes is available at the site of the synapse as it is the case in the presence of BPAPs. With an appropriate choice of parameters, Hebbian synaptic plasticity has intrinsic normalization properties that stabilizes postsynaptic firing rates and leads to subtractive weight normalization.
Generalized IntegrateandFire Models of Neuronal Activity Approximate Spike Trains of a . . .
"... We demonstrate that singlevariable integrateandfire models can quantitatively capture the dynamics of a physiologicallydetailed model for fastspiking cortical neurons. Through a systematic set of approximations, we reduce the conductance based model to two variants of integrateandfire mode ..."
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Cited by 58 (14 self)
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We demonstrate that singlevariable integrateandfire models can quantitatively capture the dynamics of a physiologicallydetailed model for fastspiking cortical neurons. Through a systematic set of approximations, we reduce the conductance based model to two variants of integrateandfire models. In the first variant (nonlinear integrateandfire model), parameters depend on the instantaneous membrane potential whereas in the second variant, they depend on the time elapsed since the last spike (Spike Response Model). The direct reduction links features of the simple models to biophysical features of the full conductance based model. To quantitatively
Noise in IntegrateandFire Neurons: From Stochastic Input to Escape Rates
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, 1999
"... We analyze the effect of noise in integrateandfire neurons driven by timedependent input, and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for timedependent subthreshold input, diffusive noise can be replaced by escape noise with a hazard funct ..."
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Cited by 41 (6 self)
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We analyze the effect of noise in integrateandfire neurons driven by timedependent input, and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for timedependent subthreshold input, diffusive noise can be replaced by escape noise with a hazard function that has a Gaussian dependence upon the distance between the (noisefree) membrane voltage and threshold. The approximation is improved if we add to the hazard function a probability current proportional to the derivative of the voltage. Stochastic resonance in response to periodic input occurs in both noise models and exhibits similar characteristics.
Dynamics of Membrane Excitability Determine Interspike Interval Variability: A Link Between Spike Generation Mechanisms and Cortical Spike Train Statistics
, 1998
"... We propose a biophysical mechanism for the high interspike interval variability observed in cortical spike trains. The key lies in the nonlinear dynamics of cortical spike generation, which are consistent with type I membranes where saddlenode dynamics underlie excitability (Rinzel & Ermentrout, 19 ..."
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Cited by 37 (4 self)
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We propose a biophysical mechanism for the high interspike interval variability observed in cortical spike trains. The key lies in the nonlinear dynamics of cortical spike generation, which are consistent with type I membranes where saddlenode dynamics underlie excitability (Rinzel & Ermentrout, 1989). We present a canonical model for type I membranes, the θneuron. The θneuron is a phase model whose dynamics reflect salient features of type I membranes. This model generates spike trains with coefficient of variation (CV) above 0.6 when brought to firing by noisy inputs. This happens because the timing of spikes for a type I excitable cell is exquisitely sensitive to the amplitude of the suprathreshold stimulus pulses. A noisy input current, giving random amplitude “kicks” to the cell, evokes highly irregular firing across a wide range of firing rates; an intrinsically oscillating cell gives regular spike trains. We corroborate the results with simulations of the MorrisLecar (ML) neural model with random synaptic inputs: type I ML yields high CVs. When this model is modified to have type II dynamics (periodicity arises via a Hopf bifurcation), however, it gives regular spike trains (CV below 0.3). Our results suggest that the high CV values such as those observed in cortical spike trains are an intrinsic characteristic of type I membranes driven to firing by “random” inputs. In contrast, neural oscillators or neurons exhibiting type II excitability should produce regular spike trains.
Dynamics of neuronal populations: The equilibrium solution
, 2000
"... you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact inform ..."
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Cited by 21 (11 self)
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you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons
 Biophys J
, 2000
"... ABSTRACT The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for tempora ..."
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Cited by 14 (0 self)
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ABSTRACT The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrateandfire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory’s predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.
Dynamics of Neuronal Populations: Eigenfunction Theory, Part 1, . . .
 NETWORK: COMPUT. NEURAL SYST
, 2003
"... A novel approach to cortical modeling was introduced by Knight et al. (1996). In their presentation cortical dynamics is formulated in terms of in teracting populations of neurons, a perspective that is in part motivated by modern cortical imaging (For a review see Sirovich and Kaplan (2002)). The ..."
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Cited by 14 (3 self)
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A novel approach to cortical modeling was introduced by Knight et al. (1996). In their presentation cortical dynamics is formulated in terms of in teracting populations of neurons, a perspective that is in part motivated by modern cortical imaging (For a review see Sirovich and Kaplan (2002)). The approach
2004b] “The influence of spike rate and stimulus duration on noradrenergic neurons
 J. Comput. Neurosci
, 2004
"... Abstract. We model spiking neurons in locus coeruleus (LC), a brain nucleus involved in modulating cognitive performance, and compare with recent experimental data. Extracellular recordings from LC of monkeys performing target detection and selective attention tasks show varying responses dependent ..."
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Cited by 14 (6 self)
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Abstract. We model spiking neurons in locus coeruleus (LC), a brain nucleus involved in modulating cognitive performance, and compare with recent experimental data. Extracellular recordings from LC of monkeys performing target detection and selective attention tasks show varying responses dependent on stimuli and performance accuracy. From membrane voltage and ion channel equations, we derive a phase oscillator model for LC neurons. Average spiking probabilities of a pool of cells over many trials are then computed via a probability density formulation. These show that: (1) Poststimulus response is elevated in populations with lower spike rates; (2) Responses decay exponentially due to noise and variable prestimulus spike rates; and (3) Shorter stimuli preferentially cause depressed postactivation spiking. These results allow us to propose mechanisms for the different LC responses observed across behavioral and task conditions, and to make explicit the role of baseline firing rates and the duration of taskrelated inputs in determining LC response.
A Simple and Stable Numerical Solution for the Population Density Equation
, 2003
"... this article, I will consider only a gaussian distribution of membrane depolarizations of magnitude p.h/ p 2 .h N h/ 2 2 2 (2.13) or the nonstochastic limit 0, in which case h/; (2.14) where .x/ is the Dirac distribution. I will refer to ..."
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Cited by 10 (2 self)
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this article, I will consider only a gaussian distribution of membrane depolarizations of magnitude p.h/ p 2 .h N h/ 2 2 2 (2.13) or the nonstochastic limit 0, in which case h/; (2.14) where .x/ is the Dirac distribution. I will refer to